In the pantheon of Donald Trump tweets, his three-part missive Wednesday morning declaring that transgender people would not be allowed in the military was not his most rude, mindless or irrational. But it is deeply troubling nevertheless. He essentially called for a step backward in time that goes counter to all the slow but necessary progress the United States has made in recent years in its treatment of transgender people.

“After consultation with my Generals and military experts, please be advised that the United States Government will not accept or allow Transgender individuals to serve in any capacity in the U.S. Military,” Trump tweeted. “Our military must be focused on decisive and overwhelming victory and cannot be burdened with the tremendous medical costs and disruption that transgender in the military would entail.”

Policy statements made on Twitter don’t generally include much thoughtful argument. But in this case, Trump offers two separate justifications that just don’t stand up. The “tremendous medical costs” for gender-transition-related healthcare are, in fact, negligibly small — an increase of between $2.4 million and $8.4 million. The military spends some $50 billion each year on healthcare, according to a Rand Corp. study.

(By way of comparison, the newspaper Military Times reported in 2015 that the Department of Defense spent $41.6 million on Viagra.)

And Trump’s assertion that transgender troops “disrupt” the military is equally specious, reminiscent of fallacious arguments made in earlier years about women, gays and lesbians. There are already 18 allied militaries around the world that allow transgender individuals to serve openly; of the four studied closely by Rand, none reported a negative impact on the operational readiness, operational effectiveness or force cohesion.